Red Rose head coach Eddie Jones is already without Saracens star Billy Vunipola for the autumn internationals against Argentina, Australia and Samoa due to a knee injury.
Harlequins director of rugby John Kingston has revealed Clifford is now set for a spell on the sidelines although it's not yet certain how long the 24-year-old will be out for following Quins' 42-26 win over Sale Sharks on Friday night.
He said: "It looks like Jack has dislocated his shoulder. It's frustrating for him because he played ever so well while he was on the pitch. But it's too early to say how long he'll be out for.
"To give an insight on where we are injury-wise, we had a training session here on Thursday night under lights and we actually had five players in doubt.
"Three of them missed and two of them got in and Jack was one of those. He had a sore biceps and pec on the left side so he had strength tablets to get out on the pitch in the first place."